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Wednesday, July 08, 2009

Is Everyone Dead Yet?

It appears that a new stage of The Wars has begun. Today I learned from our friend Mottle that string theory has officially taken over condensed matter physics and its views on quantum gravity, with the AdS/CMT correspondence. Here is one of the crucial papers under discussion. Unsurprisingly, this has generated comments elsewhere. Mottle says:

If you don't know, string theory has won the string wars

Given it's ability to completely swallow competing ideas, like a Taniwha, one can only conclude that Mottle is basically correct, but the accuracy of his statement would probably be improved by inventing a new term for string theory, to capture its latest metamorphosis into a background independent, holographic, information theoretic fermi liquid theory.

8 Comments:

Because AdS has a negative cosmological constant (not the positive one observed) which would cause cosmological attraction (not the repulsion and outward acceleration observed by Perlmutter et al. from 1998 onwards), AdS is junk cosmology.

I love the Maldacena's holographic correspondence, where physics on a brane with n dimensions is related to physics on a bulk with n + 1 dimensions. It really is nice to know that 11 dimensional supergravity isn't inconsistent with 10 dimensional superstring, because of this correspondence. Similarly, it's nic that 5-d AdS is the bulk for a 4-d CFT, QCD or condensed matter theory. Wonderful. Just a shame that no physical system is exactly represented by this stuff.

I notice on the comments to the Woit blog page you link to that someone is claiming that because AdS/CFT is an exact correspondence, all applications of it are exact and not approximations. The failure of mathematics in modern physics is that it doesn't represent anything exactly. Even the most precise calculations ever made, like the magnetic moments of muons and the Lamb shift, are only known to 15 decimals after decades of work, due to the fact that the expression is a perturbative expansion with an infinite number of terms of ever increasing loop complexity.

Even in quantum mechanics, there are no exact wave function solutions beyond hydrogen, and the exact wave function solutions to hydrogen ignore perturbative corrections for quantum field effects. So I'm depressed that Peter Woit wrote yesterday:

"I firmly believe that at a fundamental level physics is based on deep mathematics ..."

I had believed that he was rational, but now it turns out he has a crazy unjustifiable belief system. If fundamental particles behave mathematical laws, you need an infinite number of terms in a perturbative expansion for every particle interaction to be solved! It's impossible that mathematics is behind nature. Nature would have to have an infinite number of computers solving the equations behind the scenes. If have a room full of air, all the world's computers would be unable to exactly simulate all the gas molecule motions and impacts in the room in real time! It's so obvious that nature is not mathematical; the maths is just an approximate description like the artist's painting of a landscape is just a description. But nobody will listen, so I agree, everyone is at least brane dead...

Nigel, you are of course correct that physics cannot be based on random mathematical arguments, or rigorous theorems. Nonetheless, some of the simple and elegant mathematics that is being investigated will undoubetedly be the new language for physics. The particular choice of Woit et al for what these simple ideas will be seems to be incredibly wrong, because category theory is important ....

When I took a course in quantum mechanics, I was surprised by the fact that not only is nothing precisely predictable because of the uncertainty principle (i.e. because of interferences between different paths where the action of the paths is not much greater than h, as Feynman says), but (apart from the application of Schroedinger's equation to hydrogen), the work of the physicist is an art: finding an approximation for a many electron high Z atom for example. You reduce the effective value of Z to allow for the screening of the nuclear charge by the electrons between the nucleus and the electron shell you are trying to do approximate calculations on. There are other tricks too. It was obvious that mathematical physics is an art, like painting a landscape, in the sense it is not mathematically exact. There are lots of different ways of making the approximations you need to do calculations, just as different artists would all produce slightly different paintings of the same thing. It's not possible even in principle to exactly predict wavefunctions for a uranium atom's electrons.

It's wonderful that string theory is finally becoming a practical art of use in physics. It's just to be hoped that at some stage, honesty will prevail and they will stop deceiving themselves that string theory is the only possible approach to quantum gravity. (Or that spin-2 gravitons and Planck scale unification are proved true because string theory incorporates them.) Sadly, they are egotists and need to believe absurdly that their art is nature, not just an approximation or guesswork model.

"The particular choice of Woit et al for what these simple ideas will be seems to be incredibly wrong, because category theory is important ...."

I'd like to see how category theory can deal with Feynman diagrams and the configuration space of the path integral. Feynman diagrams are limited to a worldsheet consisting of 1 spatial and 1 time dimension, so they don't clearly represent the three dimensional interactions in the configuration space of the path integral. I'd hope that whatever theory supersedes the existing QFT, will make QFT easier for everybody to understand, such as school kids, what the interactions are. This is part of the problem with the stringy maths and Woit's belief: if it were true then we would end up with a "final theory" that only a few elite mathematicians would be able to understand.

David Halliday and Robert Resnick state in Physics:

"If the [Newtonian] force laws had turned out to be very complicated, we would not be left with the feeling that we had gained much insight into the workings of nature."

Sir Michael Atiyah also wrote on this topic in his Nature article, "Pulling the Strings":

"The mathematical take-over of physics has its dangers, as it could tempt us into realms of thought which embody mathematical perfection but might be far removed, or even alien to, physical reality."